Gianfranco Zola had the brightest smile on his face after the final whistle as his charges extended their unbeaten run.
The Gunners too made it ten games unbeaten, but that was scant consolation for Arsene Wenger who saw it as two points lost.
Arsenal showed the most attacking energy, but West Ham, marshalled by former Gunner Matthew Upson, had an answer for whatever the Arsenal strikers had to offer.
Both Arsenal and West Ham have proven hard to beat over the last few weeks. They have also been among the Premier League's best passing teams and so it would be difficult to predict what sort of game would be on offer.
The first half saw the Gunners dominate possession but only had an Abou Diaby header that shaved the top of the bar to show for their endeavours.
West Ham for their part showed little attacking desire, so much so that Manuel Almunia was not forced in to any action at all.
The second half showed more promise. West Ham looked a little more adventurous, but then began to sit back as the Gunners camped in the visitors half.
Arsenal should have been rewarded just before the hour when a burst on the right by Bacary Sagna culminated with a cross into the box.
Emmanuel Adebayor slid in front of his marker but somehow directed the ball well wide when it seemed easier to score.
Denislon saw his shot fly just wide shortly after but the Gunners could not break through with the combination of Nicklas Bendtner and Adebayor being decidedly unproductive.
Wenger introduced top scorer Robin van Persie in the 68th minute in an effort to break the Hammers down.
Gianfranco Zola also looked to his bench to add some attacking impetus and brought on new boy Savio Nsereko for Mark Noble on 70 minutes, but to little avail.
Adebayor, for once, got away from Upson in the 72nd minute and met Carlos Vela's cross from the left but his header was directed straight at Rob Green.
The Gunners has a good claim for a penalty on 75 minutes when Vela cut into the area. His progress was halted when he was the meat in between a West Ham defensive sandwich but referee Steve Bennett waved play on.
As full-time drew nearer, Arsenal's plight worsened when Diaby was stretchered off.
With Cesc Fabregas still at least a month away from a return, Wenger's midfield options were further restricted.
Ultimately it was a disappointing afternoon for the Gunners and a frustrating one for Wenger but the West Ham fans went home happy.